rcc is provided by qtbase5-dev-tools, which cannot be coinstalled alongside
other architectures' version of itself:

# apt install qtbase5-dev-tools:armhf
Reading package lists... Done
Building dependency tree
Reading state information... Done
The following packages will be REMOVED:
qtbase5-dev-tools
The following NEW packages will be installed:
qtbase5-dev-tools:armhf
0 upgraded, 1 newly installed, 1 to remove and 0 not upgraded.
Need to get 651 kB of archives.
After this operation, 985 kB disk space will be freed.
Do you want to continue? [Y/n] q

And the project builds and runs fine on the Raspberry Pi, using a kit and two
simple overrides in the .pro, all build dependencies as packaged by Debian,
and a toolchain that entirely runs on native code.

So is the need for the QMAKE_CXX and QMAKE_LINK overrides in the .pro.

Still, this way I could remove qemu-user-static from my system and the
project still builds on my laptop and runs on my Raspberry Pi.

The qemu dependency is not needed anymore, the rest of the problems still
stand. I wonder, since I'm rebuilding qmake, if there's a way to tell it to
use the compilers I want, and the tools I want, removing the need for the dirty
hack and the overrides in the .pro files.

qtwebengine5-dev

How about the other project that depends on qtwebengine5-dev?

# apt install qtwebengine5-dev qtwebengine5-dev:armhf
Reading package lists... Done
Building dependency tree
Reading state information... Done
qtwebengine5-dev is already the newest version (5.7.1+dfsg-6.1).
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:
The following packages have unmet dependencies:
qtwebengine5-dev:armhf : Depends: libqt5webengine5:armhf (= 5.7.1+dfsg-6.1) but it is not going to be installed
Depends: libqt5webenginecore5:armhf (= 5.7.1+dfsg-6.1) but it is not going to be installed
Depends: libqt5webenginewidgets5:armhf (= 5.7.1+dfsg-6.1) but it is not going to be installed
E: Unable to correct problems, you have held broken packages.

It turns out that something in the big chain of dependencies of
qtwebengine5-dev makes the amd64 and armhf versions not coinstallable.

It seems that I have to abandon the idea of installing armhf build-dependencies
in the main development system, and I need to start considering to leave the
host system untouched to do the native builds, and use a chroot for the
cross-compilers and the cross-build-dependencies.